Download 7. Quadrilateral

Class – VII
QUADRILATERALS
Quadrilateral is a polygon of four sides. It is a figure formed by joining four points in an order
(no three points are collinear). A quadrilateral has four sides, four angles and four vertices.
Types of Quadrilaterals
1. Trapezium: A quadrilateral with at least one pair of opposite sides parallel is called
trapezium.
2. Parallelogram: A quadrilateral with both pairs of opposite sides parallel is called
parallelograms.
3. Rhombus: A parallelogram having all sides equal is called rhombus.
4. Rectangle: A parallelogram with one angle a right angle is called rectangle.
5. Square: A parallelogram having all sides equal and one angle a right angle is called square.
6. Kite: A quadrilateral with two pairs of adjacent sides equal, but opposite sides are not
parallel, is kite.
D
A
D
C
Trapeziu
m
AB | | CD
B
A
Parallelogra
m
B
AB | | CD & AD | |
BC
D
C
A
Rhombu C
s
B
C
D
RECTANGL
A
E
D
SQUAR
A
C
C
E
B
D
KITE
B
B
From above definitions, we can conclude
A
1. Square, Rectangle and rhombus are all parallelogram.
2. Kite is not a parallelogram.
3. A trapezium is not a parallelogram.
4. A parallelogram is a trapezium.
5. A square is a rectangle and also a rhombus.
6. A rectangle or a rhombus is not a square.
Properties of Quadrilaterals:
1. A diagonal of a parallelogram divides it into two congruent triangles.
(Theorem 8.1)
2. In a parallelogram
(a) Opposite sides are equal.
(Theorem 8.2)
(b) Opposite angles are equal.
(Theorem8.4)
(c) The diagonals bisect each other.
(Theorem 8.6)
3. A quadrilateral is a parallelogram
(a) If each pair of opposite sides of a quadrilateral are equal.
(Theorem 8.3)
(b) If each pair of opposite angles are equal.
(Theorem 8.5)
(c) If the diagonals of a quadrilateral bisect each other.
(Theorem8.7)
(d) If a pair of opposite sides is equal and parallel.
(Theorem 8.8)
4. Diagonals of a rectangle bisect each other and are equal.
5. Diagonals of a rhombus bisect each other at right angles.
6. Diagonals of a square bisect each other at right angles and are equal.
7. Quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a
parallelogram
8. Quadrilateral formed by joining the mid-points of the sides if a rhombus is a rectangle.
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9. The line segment joining the mid-point of two sides of a triangle is parallel to the third
side.(Theorem 8.9)
10.The line drawn through the mid-point of one side of a triangle, parallel to another sides
bisects the third side. (Theorem 8.10)
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________________________________________________________________________________________
Address : 61, First Floor, Chanakya Plaza, New CG Road, Chandkheda, Ahmedabad
Contact : 96017 55017 , 90999 66717
www.abhigyanam.com